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- 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.Need help with parts d and k. Data: TSERofReturn AcmeRofReturn 1 0.42478 -0.48194 2 1.61213 -0.73284 3 -0.98754 -2.28445 4 -0.30013 -1.55312 5 1.41215 0.68674 6 0.68725 -1.31132 7 0.03733 -0.83295 8 -1.72494 -1.71975 9 0.33729 1.14443 10 -1.07502 -1.79885 11 0.86222 0.89736 12 1.17468 1.66664 13 -0.38761 -0.02658 14 1.66212 0.9086 15 1.09969 1.99935 16 -0.06266 0.46148 17 -1.96241 -1.41004 18 -1.32499 -0.38086 19 -1.51247 -1.90904 20 0.74974 0.91873 21 -0.38761 -0.49714 22 -0.17514 -1.31385 23 -3.41222 -1.15681 24 -0.01266 2.11718 25 0.16231 1.78766 26 -0.82506 1.30344 27 -0.41261 -0.43377 28 0.2623 -1.70274 29 -1.16251 0.4692 30 -1.05003 0.27671 31 -0.65008 -0.63741 32 0.62475 2.9895 33 -0.68758 1.3613 34…
- 4) Here are data on the lengths of male and female roaches (in mm). Your job is to find out if there is adifference between male and female roaches (this should be two sided - why?).males 15.4 13.9 12.7 9.6 6.6 10.7 9.9 13.3 16.2 9.0 11.4 16.6 12.2females 16.7 16.3 12.8 16.9 15.1 12.8 18.7 18.3 8.6 13.6 15.3 16.2 13.4It's up to you to figure out what the best procedure is, what kind of hypotheses to use, which α to use,what test to use, and so on. Make sure you follow all the appropriate steps. You should probably use Ras you’ll get done much quicker. Remember to very clearly state your results in writing. Never turn in just an R printout .Hint: how do you decide which test to use? What kind of distributions do the data have?A group of 11 students was selected at random and asked for their high school GPA and their freshmen GPA in college the subsequent year. The results were: Student High School GPA Freshmen GPA 1 2.0 1.6 2 2.2 2.0 3 2.6 1.8 4 2.7 2.8 5 2.8 2.1 6 3.1 2.0 7 2.9 2.6 8 3.2 2.2 9 3.3 2.6 10 3.6 3.0 We would like to know whether there is a linear relationship between the high school GPA and the college freshmen GPA, and we would like to be able to predict the freshmen GPA, if we know that the high school GPA of another student is, say, 3.4. Provide the two requested scatter plots for this data (put college freshman GPA on the Y (vertical) axis!). a) What would be your approximate 95% prediction interval for question (g)? b) Show your scatterplot with the predicted trend line belowConsider the linear model Yi = B0 + B1X1i + B2X2i + ui where ui is the error term and where E(ui|X1i,X2i) = 0, observations (Yi,X1i,X2i) are independent and identically distributed, 0 < E(Y4) < 1, 0 < 1i E(X14i) < 1, 0 < E(X24i) < 1 and where X2i = X12i. Are the OLS estimators Bˆ1 and Bˆ2 of the coe¢cients B1 and B2 unbiased and consistent? Explain.
- (Please answer 2nd question ) 1. Assume that there are two types of driver: One is careful and has a 0.1% of being in an accident. The other type is careless and has a 1% chance of being in an accident. Assume that each type represents 50% of the population. If there is a law mandating that all drivers buy insurance that would cover $100,000 in damages, the actuarially far premium for all drivers would be ________ while if there were no such law, the fair premium would be __________. Group of answer choices A) $100, $1,000 B) $100, somewhere between $100 and $1,000 C) $550, somewhere between $550 and $1,000 D) $550, 1,000 Ans :- option c ). 2. The term(s) used to describe the problem(s) that make the actuarially fair premiums different in the two cases in the question above is(are) Group of answer choices A) Asymmetric information B) Moral hazard C) Adverse selection D) A, B, and C E) A and CConsider the following clustering problem that has a single variable X. What is the complete linkage dissimilarity measure (based on the usual Euclidean distance) between the two clusters {1, 4.2, 5.3} and {7.1, 9}? (Hints: The cluster {1, 4.2, 5.3} corresponds to three observations of X grouped together where X=1 for the first observation, X=4.2 for the second and X=5.3 for the third. Similarly, the cluster {7.1, 9} corresponds to two observations of X grouped together. Finally, the Euclidean distance between two different points x1 and x2 is obviously here the absolute value of the difference, in other words |x1-x2| )An industrial concern has experimented with several different mixtures of the fourcomponents—magnesium, sodium nitrate, strontium nitrate, and a binder—that comprise arocket propellant. The company has found that two mixtures, in particular, give higher flare illumination values than the others. Mixture 1 consists of a blend composed of the proportions.40, .10, .42, and .08, respectively, for the four components of the mixture; mixture 2 consists ofa blend using the proportions .60, .25, .10, and .05. Twenty different blends (10 of each mixture)are prepared and tested to obtain the flare-illumination values. These data appear here (in unitsof 1,000 candles).Mixture 1 185 192 201 215 170 190 175 172 198 202Mixture 2 221 210 215 202 204 196 225 230 214 217a. Plot the sample data. Which test(s) could be used to compare the meanillumination values for the two mixtures?b. Give the level of significance of the test and interpret your findings
- Question No. 4: According to the All Pakistan Software Developer Association (APSDA), developers generally spend more than 40 hours each week working on software and web development. The Table 4.1 shows the number of hours worked per week for a sample of 15 Software developers and a sample of 10 Web developers. Table 4.1 Software Developers 56 54 54 49 61 48 58 60 59 53 50 58 55 57 52 Web Developers 47 50 46 47 48 49 46 55 44 42 ---- a) What is the third quartile of spending working hours for Software developers? b) Create a box plot for the number of hours worked for Software developers. c) Create a box plot for the number of hours worked for Web developers. d) Comment on the differences between the box plots for Software & Web developers.A study is made for a particular allergy medication in order to determine the length of relief it provides Y (in hours) in relation to the dosage of medication X (in mg). For this reason, ten patients were given different doses of the medication and were asked to report back when the medication seemed to wear off. Patient #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 Dosage (x) Relief Hours (y) 3 3.5 4 5 6 6.5 7 8 8.5 9 9.1 5.5 12.3 9.2 14.2 16.8 22.0 18.3 24.5 22.7 (i) Draw a scatter diagram. (ii) Calculate the product moment correlation coefficient and comment on your answer. (iii) Construct the least squares regression line.A rural county presently uses Asphalt A to pave its highways, but is considering using themore expensive Asphalt B (which is reported to be more durable). The two types of asphaltare tested using 200m test strips on five different two-lane highways. On each test strip, arandomly selected lane was paved with Asphalt A and the lane in the opposing direction waspaved with Asphalt B. It has been determined that it is more economical to use Asphalt B ifthe length of time before resurfacing is required (i.e. longevity) is at least 2.5 years longer onaverage than that of Asphalt A. Assume that the longevity of each type of asphalt is normally distributed. Using a 2% significance level and assuming that the data for the two types of asphalt at eachtest strip can be paired, determine if Asphalt B lasts at least 2.5 years longer than Asphalt Aon average. Location 1 2 3 4 5Asphalt A 11.2 9.0 10.7 11.4 8.5Asphalt B 18.8 11.7 19.9 19.0 13.4
